I'm pondering the characteristics of similar but not identical transformers in series. Specifically, with the primaries in parallel and the secondaries in series. Assume that all the secondary winding are have the same current rating, but the cores have slightly different reluctances and primary current ratings ratings.

What will limit the current of short circuiting the series string of secondaries?
For the purpose of choosing the current rating required by the secondary coils.

How I think this could go:

I would like to think we could use conservation of energy and divide the total input power by the open voltage of the secondary string, to get the ideal maximum current. Although, that seems to simple..

Otherwise I suppose the current would be limited by the 'weakest' transformer. If so I suppose the voltage contribution from the weak transformer would drop as the other transformers provide a higher amount of current. That also doesn't seem like the complete picture, then the current would be determined be the strongest transformer and there would be some voltage much lower than the original open circuit, but a bit bigger than if the strongest transformer was on its own.

The magnetising and primary coil impedance can be referred to the secondary so its combined with the secondary impedance. Then, the equivalent impedance of the secondaries in series is summed for the total output impedance. To solve for the short circuit current its simply ohms law with the open circuit voltage.

Where does the reluctance of the core come into it? Does it increase impedance in series or parallel with the primary, when using the standard primary referred equivalent transformer model? I suppose an increase in core reluctance would be seen as an increased inductance on the primary.